1. Field of the Invention
The invention relates to a method for determining an electric voltage u(t) and/or an electric current i(t) of a RF signal on an electric cable in a calibration plane through measurement in the time domain using a time domain measuring device, whereby the calibration plane is designed such that a device under test can be connected electrically with the calibration plane. In a measuring step, using a directional coupler, a first component v3(t) of a first RF signal which, starting out from a signal input, runs in the direction of the calibration plane through the directional coupler, is decoupled, fed to the time domain measuring device at a first measuring input and measured there in a first measuring plane, and a second component v4(t) of a second RF signal which, starting out from the calibration plane, runs in the direction of the signal input through the directional coupler, is also decoupled using the directional coupler, fed to the time domain measuring device at a second measuring input and measured there in a second measuring plane. The signal components v3(t), v4(t) measured using the time domain measuring device are, by means of a first mathematical operation, transformed into the frequency domain as wave quantities V3(f) and V4(f), then absolute wave quantities a2 and b2 in the frequency domain are determined in the calibration plane from the wave quantities V3(f) and V4(f) using calibration parameters, and fmally the calculated absolute wave quantities a2 and b2 are, by means of a second mathematical operation, converted into the electric voltage u(t) and/or the electric current i(t) of the RF signal in the time domain in the calibration plane. In a preceding calibration step, the calibration parameters are determined in such a way that they link the wave quantities V3(f) and V4(f) in the measuring planes mathematically with the wave quantities a2 and b2 in the calibration plane.
2. Description of Related Art
One of the most important measuring tasks in radio frequency and microwave technology involves the measurement of reflection coefficients or generally—in the case of multiports—the measurement of scattering parameters. The linearly-describable network behavior of a device under test (DUT) is characterized through the scattering parameters. Frequently, it is not only the scattering parameters at a single measuring frequency which are of interest, but their frequency-dependency over a finitely broad measuring bandwidth. The associated measuring method is referred to as network analysis. Depending on the importance of the phase information in the measuring task in question, the scattering parameters can either be measured solely in terms of amount or also as a complex measurement. In the first case one speaks of scalar network analysis, in the second case of vectorial network analysis. Depending on the method, number of ports and measuring frequency range, the network analyzer is a more or less complex system consisting of test signal source and receivers which function according to the homodyne or the heterodyne principle. Because the measuring signals have to be fed to the device under test and back again through cables and other components with unknown and non-ideal properties, in addition to random errors, system errors also occur in network analysis. Through calibration measurements, the aim of which is to determine as many as possible of the unknown parameters of the test apparatus, the system errors can, within certain limits, be reversed. Very many methods and strategies exist here which differ considerably in the scope of the error model and thus in complexity and efficiency. (Uwe Siart; “Calibration of Network Analysers”; 4 Jan. 2012 (Version 1.51); http://www.siart.de/lehre/nwa.pdf).
However, scattering parameters measured in such a calibrated manner only fully describe linear, time-invariant devices under test. The X parameters represent an expansion of the scattering parameters to non-linear devices under test (D. Root, et al: “X-Parameters: The new paradigm for describing non-linear RF and microwave components.” In: tm—Technisches Messen No. 7-8, Vol. 77, 2010), which are also defined through the frequency. However, each device under test can also be described through measurement of the currents and voltages or the absolute wave quantities at its ports within the time domain. The measurement in the time domain inherently includes all spectral components resulting for example from the non-linearity as well as the change over time of the device under test or its input signals. Such a time domain measurement also requires calibration. However, in order to measure absolute values the aforementioned calibration methods cannot be applied without modification, since they only permit the determination of relative values (scattering parameters).
A high frequency circuit analyzer which is used to test amplifier circuits is known from WO2003/048791 A2. A microwave transition analyzer (MTA) with two inputs measures two independent signal waveforms, for example the propagated and reflected wave, via signal paths and ports in the time domain while the amplifier circuit under test is connected. The measured waves are further processed by means of calibration data in order to compensate for the influence of the measurement system on the waves between the ports of the amplifier circuit and the input ports of the MTA. The MTA is again used in order to determine the calibration data, measuring signals in the time domain while the calibration standards are connected. These signals in the time domain are converted into the frequency domain using an FFT and the calibration data are then determined. Since only periodic signals in the time domain are measured, the signals are converted to a lower-frequency intermediate frequency prior to measurement.
The document WO2013/143650 A1 describes a time domain measuring method with calibration in the frequency domain according to the preamble of claim 1. In this method, an electric voltage and/or an electric current of a high frequency signal are measured in the time domain on an electric conductor in a calibration plane. For this purpose, a directional coupler is inserted in the line supplying the measurement signal to the device under test, and a first component of the first HF signal, which runs from the signal input of the directional coupler through the directional coupler in the direction of the device under test, is decoupled via the first measuring output of the directional coupler and measured using the time domain measuring device, and a second component of the HF signal returning from the device under test, which runs in the opposite direction through the directional coupler, is decoupled via the second measuring output of the directional coupler and measured using the time domain measuring device. The measured signal components are transformed into the frequency domain in order to obtain wave quantities. With the aid of previously determined calibration parameters, corresponding wave quantities in the calibration plane are determined in the frequency domain from these wave quantities determined in the measuring planes, and these wave quantities are then in turn transformed back into the time domain, so that they state the signal values u(t) and/or i(t) in the time domain which are to be determined in the calibration plane.
The calibration parameters which link the wave quantities in the measuring planes with the wave quantities in the calibration plane are, in a preceding calibration step, determined in a frequency-dependent manner with the aid of a calibration device, whereby the calibration step is described in detail in the cited document WO2013/143650 A1. These calibration parameters can be represented in the form of an error matrix
  E  =      (                                        e            00                                                e            01                                                            e            10                                                e            11                                )  with which the wave quantities a2, b2 in the calibration plane can be calculated as follows from wave quantities b4, b3 in the measuring planes:
      (                                        b            4                                                            b            2                                )    =            (                                                  e              00                                                          e              01                                                                          e              10                                                          e              11                                          )        ⁢                  (                                                            b                3                                                                                        a                2                                                    )            .      The disclosing content of WO2013/143650 A1 is, with respect to the determination of the calibration parameters, herewith included in this description through express reference.
However, it has transpired that the signal values in the calibration plane determined by means of this method are not always exact and can depend on the time domain measuring device used.
Known from WO-A-2013 143 650 is a method for determining an electric voltage and/or an electric current of an RF signal on an electric conductor in a calibration plane through measurement in the time domain using a time domain measuring device, wherein a device under test can be connected electrically with the calibration plane. In a measuring step, using a directional coupler, a first component of a first RF signal which, starting out from a signal input, runs in the direction of the calibration plane through the directional coupler, is decoupled, fed to the time domain measuring device at a first measuring input and measured there. A second component of a second RF signal which, starting out from the calibration plane, runs in the direction of the signal input through the directional coupler, is fed to the time domain measuring device at a second measuring input and measured there. The signal components are, by means of a first mathematical operation, transformed into the frequency domain as wave quantities, then from these wave quantities absolute wave quantities in the frequency domain are determined in the calibration plane using calibration parameters, and finally the determined absolute wave quantities are, by means of a second mathematical operation, converted into the electric voltage and/or the electric current of the RF signal in the time domain in the calibration plane, wherein the calibration parameters link the wave quantities mathematically with the absolute wave quantities in the calibration plane.
The document Clement T. S. et al: “Calibration of Sampling Oscilloscopes With High-Speed Photodiodes,” IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, IEEE SERVICE CENTER, PISCATAWAY, N.J., US, vol. 54, no. 8, 1 Aug. 2006 (2006-08-01), pages 3173-3181, XP-001545193, ISSN: 0018-9480, DOI: 10.1109/TMTT.2006.879135 section: C. Impedance Mismatch Correction discloses the determination of reflection coefficients of a photodiode and an oscilloscope with the aid of a network analyzer.
The document Arkadiusz Lewandowski et al: “Covariance-Based Vector-Network-Analyzer Uncertainty Analysis for Time and Frequency-Domain Measurements”, IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, IEEE SERVICE CENTER, PISCATAWAY, N.J., US, vol. 58, no. 7, 1 Jul. 2010 (2010-07-01), pages 1877-1886, XP-011311287, ISSN: 0018-9480, section: IV. Propagating Covariance-Matrix-Based Uncertainties subsection; A Mismatched-Correcting Waveform Measurements discloses the determination of an output impedance of the signal source and an input impedance of the oscilloscope using a network analyser, whereby the equation used is only valid for low frequencies, but not for high frequencies.
The document WO-A-2008 016699 discloses the determination of various parameters for various components such as test prods or cables.